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Abstract We develop a thin-film microstructural model that represents structural markers (i.e., triple junctions in the two-dimensional projections of the structure of films with columnar grains) in terms of a stochastic, marked point process and the microstructure itself in terms of a grain-boundary network. The advantage of this representation is that it is conveniently applicable to the characterization of microstructures obtained from crystal orientation mapping, leading to a picture of an ensemble of interacting triple junctions, while providing results that inform grain-growth models with experimental data. More specifically, calculated quantities such as pair, partial pair and mark correlation functions, along with the microstructural mutual information (entropy), highlight effective triple junction interactions that dictate microstructural evolution. To validate this approach, we characterize microstructures from Al thin films via crystal orientation mapping and formulate an approach, akin to classical density functional theory, to describe grain growth that embodies triple-junction interactions. 

Synopsis Mammals exhibit a diverse range of limb morphologies that are associated with different locomotor ecologies and structural mechanics. Much remains to be investigated, however, about the combined effects of locomotor modes and scaling on the external shape and structural properties of limb bones. Here, we used squirrels (Sciuridae) as a model clade to examine the effects of locomotor mode and scaling on the external shape and structure of the two major limb bones, the humerus and femur. We quantified humeral and femoral morphologies using 3D geometric morphometrics and bone structure analyses on a sample of 76 squirrel species across their four major ecotypes. We then used phylogenetic generalized linear models to test how locomotor ecology, size, and their interaction influenced morphological traits. We found that size and locomotor mode exhibit different relationships with the external shape and structure of the limb bones, and that these relationships differ between the humerus and femur. External shapes of the humerus and, to a lesser extent, the femur are best explained by locomotor ecology rather than by size, whereas structures of both bones are best explained by interactions between locomotor ecology and scaling. Interestingly, the statistical relationships between limb morphologies and ecotype were lost when accounting for phylogenetic relationships among species under Brownian motion. That assuming Brownian motion confounded these relationships is not surprising considering squirrel ecotypes are phylogenetically clustered; our results suggest that humeral and femoral variation partitioned early between clades and their ecomorphologies were maintained to the present. Overall, our results show how mechanical constraints, locomotor ecology, and evolutionary history may enact different pressures on the shape and structure of limb bones in mammals.